NATIONAL OPEN UNIVERSITY OF NIGERIA SCHOOL OF SCIENCE AND TECHNOLOGY COURSE CODE: PHY320 COURSE TITLE: LABORATORY PHYSICS

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1 A Study of Network Theorems NATIONAL OPEN UNIVERSITY OF NIGERIA SCHOOL OF SCIENCE AND TECHNOLOGY COURSE CODE: PHY30 COURSE TITLE: LABORATORY PHYSICS

2 Physics Laboratory II Course Code Course Title Course Developer PHY30 LABORATORY PHYSICS Dr. A. B. ADELOYE DEPARTMENT OF PHYSICS FACULTY OF SCIENCE UNIVERSITY OF LAGOS Programme Leader Dr. Ajibola S. O. National Open University of Nigeria Lagos

3 A Study of Network Theorems (For Counsellor's use only) Grade... Evaluated by. Name..... Enrolment Number EXPERIMENT A STUDY OF NETWORK THEOREMS Structure. Introduction Objectives. Apparatus.3 Study Material.4 Precautions.5 Experiments Maximum Power Theorem Superposition Theorem Reciprocity Theorem Thevenln's Theorem.6 Conclusions. INTRODUCTION Electric circuits form the backbone on which the study of most electrical phenomena is based. These circuits may contain resistors, capacitors, inductors which are passive elements, or some active devices such as vacuum tubes, transistors etc. In order to understand the nature of the circuits and their applications, one is required to perform the analysis for currents, voltages, power or frequency responses in the circuit. If the circuit is simple, one can do the analysis just using Ohm's Law. However, many circuits are complicated and analysis becomes difficult. Hence systematic methods should be developed to simplify the circuits and to make the analysis easy. In order to perform the analysis of a complicated circuit in a simplified manner, some theorems have been developed. These theorems are known as Network Theorems. Objectives After performing the experiments, you will be able to: verify maximum power, superposition, reciprocity and Thevenin's theorems. apply above theorems to different networks.. APPARATUS Two transistorised power supplies (0 5V), resistors ( ohms) multimeters, connecting wires..3 STUDY MATERIAL Before performing the experiments you may be interested in knowing more about a network and the theorems mentioned in the Objectives..3. Network An electrical network is any interconnection of electric circuit elements such as inductors, resistors, capacitors, generators, or branches where each branch may include R, L, C, or other types of linear elements. A linear element is one in which the current is proportional to the voltage. Such a linear network having two distinct pairs of terminals is called a four-terminal network, :,. as shown in Fig...a. However if one of the, terminals is common to the 3

4 Physics Laboratory II, pair, the circuit is known as 3-terminal network as shown in Fig. l.l.b. If the, terminals are short circuited, it becomes a two-terminal network. Networks may be of the following types: Fig...a 4-Terminal Network Fig...b 3-Terminal Network PASSIVE NETWORK: A network containing circuit elements without any energy source such as a battery is known as passive network. ACTIVENETWORK: A network containing generators or energy sources along with other elements is known as an active network. A specific path between two points in a network is called a branch. In a network a set of branches forming a closed path in such a way that if one branch is omitted the remaining branches do not form a closed path, is known as a Mesh. A terminal of any branch of network, or a terminal common to two or more branches is known as a Node or Junction. We can now summarise that a network may have active or passive elements, branches, nodes, meshes. Our aim is to analyse any such network for current in any loop, or the voltage across any element using appropriate network theorems. We will first try to understand some of the important network theorems and then proceed further for their applications using practical network circuits..3. Superposition Theorem: Let us consider the following circuits. Fig.. 4

5 A Study of Network Theorems A battery of volt applied to a resistance of 00 ohms, causes a current of /00 ampere to flow. Two batteries in series, each of volt connected to the same 00 ohm resistance, each cause /00 ampere to flow. Together they cause /00 ampere to flow. The total current is thus the sum of the currents produced by the individual batteries. This statement if generalised is known as the Superposition Theorem. This can be stated as follows. Each emf in a linear network produces current in any given branch Independent of the action of other emf s, and that the resultant total current in any branch is the algebraic sum of the contribution of current due to each of the emfs. You will be able to verify this theorem by performing the experiment. SAQ In the following circuit calculate the current caused to flow through the resistor due to the individual sources separately. Calculate the current when both sources are present. Verify your result experimentally, later on. Fig..3 Answer: With V alone, the current expected is... With V alone the current is... With both V and V, the current expected is Reciprocity Theorem: The reciprocity theorem states that if an emf E is placed in one branch of an electrical circuit, giving rise to a current I in another branch, the same current I is obtained in the original branch when the emf E is transferred to the branch where the current I arose. In order to understand clearly, let us consider the following circuit, as an example. Fig..4.a Fig..4.b The Reciprocity Theorem assures that I I 3 since E is the same in each circuit. 5

6 Physics Laboratory II.3.4 Thevenin's Theorem: Let us consider a simple circuit as shown in Fig..5. Fig..5 If you want to find out the current through the load R you can apply Ohm's Law and get I E / R. However if the circuit (outlined in dashes) is complicated such as shown in Fig..6, it is difficult to find the current or the voltage across the load R L using Ohm's Law. In order to analyse such circuits, Thevenin s Theorem is used. This theorem states that any two terminal linear network containing energy sources and impedances can be replaced with an equivalent circuit consisting of a voltage source E ' in series with an impedance R'. The value of E ' is the open circuit voltage between the terminals of the network and R' is the impedance measured between the terminals with all energy sources eliminated (but not their impedances). Thus the Thevenin's equivalent circuit of the above network is shown below. Fig..7 6

7 A Study of Network Theorems We will study the application of Thevenin's Theorem in a network while performing the experiment..4 PRECAUTIONS: (a) (b) (c) Before using the power supply make sure that you are getting the necessary voltage range, by measuring with the multimeter. Before using the resistance make sure of their values, by measuring with a multimeter. Before using the Ammeter and Voltmeter check for zero setting..5 EXPERIMENTS.5. Verification of Maximum Power Transfer Theorem APPARATUS: Power supply (0 V dc), multimeter, resistors: 00 ohms, 00 ohms, 300 ohms, 400 ohms, 500 ohms, 600 ohms, 800 ohms, 000 ohms (nominal values). PROCEDURE: Arrange the circuit as shown in Fig..8. Make R = 500 ohms, and R L 00 ohms. Connect a voltmeter across the load to measure the voltage drop across the load ( R L ). Keep the output of the power supply at 0V with the output-varying knob. Note the voltage across the load resistor in Observation Table I, Now replace the load resistor by another resistor of different value and measure the voltage across it. Make V = 0 volts by adjustment, before you measure and note the value of voltage across R L. Repeat the experiment with at least 8 different resistors. In each case record your measurements in the Observation Table I. Fig..8 7

8 Physics Laboratory II OBSERVATION TABLE I Value of source impedance (R) = 500 ohms Source voltage (V) = 0 volts. S. No. Load Resistance (R L ) ohms Output voltage V Volts 0 Power Transfer (calculate) P V0 / R L Watts Now plot a graph between load resistance P O W E R RL and the power transferred. LOAD RESISTANCE With the help of the graph explain your result and record your findings in the space below. What do you observe from the nature of the graph? What is the condition for maximum power transfer? SAQ When the maximum power is transferred from source to the load, then the output voltage V 0 compared to V? More? Less? Somewhat is the write your choice & your comments: 8

9 A Study of Network Theorems.5. Application of Superposition Theorem APPARATUS Two voltage sources, a multimeter, and three resistors 500 ohms each. PROCEDURE STEP : Connect the circuit as shown in Fig.l.9.a. Set V about 0 volts, and V about 5 volts. Before Turning on the power supplies, calculate the current expected. Write the value here... Choose an appropriate multimeter range, and turn on the power supplies. Record the supply voltage in each loop and the current in the first loop. Record the current as I a, in Observation Table II. Repeat Step three times. Fig..9.a Fig.l.9.b Fig..9.c STEP : Now change the circuit to that of Fig.l.9.b. With V at the same value, note the current in the first loop as I b. Repeat Step three times. STEP 3: Now change the circuit to that of Fig..9.c. With V the same as in STEP, note the current in the first loop as I c. Repeat step 3 three times. Repeat the three steps for V = 5 volts and V = 5 volts. 9

10 Physics Laboratory II Repeat the three steps for V = volts and V = 6 volts. All readings should be recorded in Observation Table II. OBSERVATION TABLE II S. No. V V I a I b I c I b I c (calculate) (volts) (volts) (amp) (amp) (amp) (amp) With the help of the results compare the values I a and I o I c, taking into account the experimental error your observe. Explain how it confirms the Superposition Theorem, in the space provided below..5.3 Verification of the Reciprocity Theorem APPARATUS Two voltage sources (0 to 0 volts), multimeter, three resistors 500 ohms each, one 000 ohms. PROCEDURE Fig..0.a 0

11 A Study of Network Theorems STEP : Arrange the circuit as shown in Fig..0.a. Set V at approximately 5 volts, and measure V and I, noting them in Observation Table III. Repeat Step three times. STEP : Now connect the circuit of Fig..0.b. Set V at approximately 3 volts and measure V and I, noting them in Observation Table III. Repeat Step three times. STEP 3: Calculate V / I and V / I and enter in the Observation Table III. Repeat Step 3 three times. Repeat the steps above, using R = 000 ohms and R = R 3 = 500 ohms. Repeat the steps again, using the same set of resistors but with V about 7 volts and V about 0 volts. OBSERVATION TABLE III S. No. V I V I V / I V / I (volts) (amps) (volts) (amps) (ohms) (ohms) How do the calculations agree with the predictions of the Reciprocity Theorem, taking into Account the experimental errors experienced? SAQ: In the above experiments, will the Theorem hold good if the two voltages V and V are present at the same time?.5.4 Application of Thevenin's Theorem APPARATUS: Variable power supply (0 to 0 V), two resistors of 500 ohms each, a variable resistor and a multimeter.

12 Physics Laboratory II Fig...a Fig...b PROCEDURE: Arrange the circuit as shown in Fig..a. Measure the current I through the load R L. Now arrange the Thevenin's equivalent circuit Fig...b by calculating the value of R' and E' as : R' R R ; R R E E' R R R Measure the current I ' through the load in the equivalent circuit. Repeat the experiment using two different pairs of resistors R and R. Record the data in Observation Table IV. Repeat the Procedure three times. OBSERVATION TABLE IV E =... Volt R L = 500 ohm S. No. R R I E ' R ' I ' Compare the values I and I '. Explain your result and record your findings in the space given below, taking into account the experiment errors experienced.

13 A Study of Network Theorems In the above experiment, calculate the values of currents I and I' using Ohms's law and compare with your measured values..6 CONCLUSIONS: After the experiments, list your findings. 3

14 Physics Laboratory II (For Counsellor's use only) Grade... Evaluated by. Name..... Enrolment Number EXPERIMENT CALIBRATION OF A THERMISTOR AND DETERMINATION OF ITS ENERGY GAP Structure. Introduction Objectives. Apparatus 3 Study Material.4 Precautions.5 Experiments.6 Conclusions. INTRODUCTION The electrical resistance of materials generally increases with increase of temperature. This increase is usually very small (< % degree C). The discovery of semiconducting materials and the techniques used in modifying their electrical properties have resulted in materials for which the variation in electrical resistance with temperature is large (as high as 3 to 0%). Such devices have very many applications in measurement and control of temperatures of objects. Thermistors are semiconductor devices, with a high (usually negative) temperature coefficient of resistance. Some thermistors have their room temperature resistance decrease 5% per degree rise in temperature. This high degree of sensitivity to temperature change, makes it possible to use the thermistor in temperature measurement and control etc. Thermistors are generally used in the temperature range of -00 C to 300 C. Thermistor have generally three important characteristics (Fig.) which are extremely useful in measurement & control applications. (i) (ii) Resistance vs Temp, characteristics (Fig.. (a)) Voltage vs Current characteristics (Fig.. (b)) Fig.. 4

15 A Study of Network Theorems In this experiment you will find the resistance temperature characteristics of a thermistor, which has a high temperature coefficient of resistance. This property is used in making temperature transducers. Thermistors are used in other fields also. Some of the important applications of transducers are in remote measurement or control, temperature controller circuits, compensator circuits and in thermal conductivity measurements etc. For example the temperature inside a vacuum furnace, measurement of super heated steam inside a turbine of a thermal power station. In the first part of the experiment you will calibrate the given thermistor using a thermocouple in the temperature range 30 C - 50 C. As you know that the thermistors are made of materials called semiconductors, we will calculate the band gap energy (See Fig..) of the semiconducting material. OBJECTIVES The student will be able to: calibrate the given thermistor using a thermocouple. calculate the band gap energy, Eg of the thermistor material (semiconductor).. APPARATUS: Thermo couple (copper - constantan) Thermistor (7 K ohms at room temperature) Water bath Oil bath Ice bath Burner or stove or an electric hot plate Wire gauze Stands Resistance Boxes (of different ranges K ohm to 3K ohm) Low voltage D.C source (battery or power supply 0-4 Volts) Galvanometer/ head phone Millivoltmeter (0 to 0 mv) Multimeter Soldering iron, soldering rosin, and solder. Connecting wires..3 STUDY MATERIAL The thermistor is a made of a semiconducting material. Its resistance generally decreases when the temperature is increased. The relation between resistance and temperature is given by: R T R0 exp( E g / kt ) Here R T R E 0 g = resistance at temperature T in Kelvin degrees. = resistance at 0 Kelvin. = the energy difference between the filled valence and the empty conduction band of the particular semiconductor (Fig..). Electrons in a free atom have discrete energy levels. But when atoms are brought together to form molecules and solids the electronic energy levels became almost continuous over certain ranges. These ranges are separated by regions of energy values that electrons cannot possess. The energy 5

16 Physics Laboratory II of the electrons in a semiconductor is represented on a one-dimensional energy diagram (see Fig..), showing ranges of energies the electrons are allowed to have and the ranges of energies in between the allowed bands where electrons are forbidden to exist. Fig..: Energy band diagram of a semiconductor The highest occupied band corresponds to the ground state of the outmost or valence electrons in the atom. For this reason the upper occupied band is called the valence band. In a semiconductor, the valence band is full or nearly so. In addition the width of the forbidden energy gap ( E, the band gap energy) between the top of the valence band and the bottom of the next allowed band, called the conduction band is of the order of ev (e.g. for Ge = 0.7 ev, and for Si = l.l ev). SAQ What do you mean by the energy gap in a semiconductor? The resistance of a thermistor may be determined at various temperatures with the help of some type of bridge circuits. In these circuits we required the use of a galvanometer or head phone as a balancing indicator. All these bridges work on the principle of the Wheatstone s bridge. The circuit arrangement is shown in Fig..3. g Fig..3 6

17 A Study of Network Theorems Wheatstone's bridge consists of four resistances R, R, R 3 and R 4 connected as shown in Fig..3 to form a network. A battery is connect between one pair of opposite junctions, A and C. A galvanometer G of resistance R is connected across the other pair of junctions B and D as a g balancing indicator along with a high resistance HR. Let I be the current from the battery entering at the junction A. Let I, I, I 3, I 4 and I g be the currents through the resistances R, R, R 3 and R 4 and galvanometer G respectively. By Kirchhoff s first law (The algebraic sum of the currents flowing into a junction is zero) we have the following relations. For the junction A, I I I 3 = 0 () For the junction B, I I I g = 0 () For the junction D, I 3 I g I 4 = 0 (3) If the bridge is balanced, the voltage at point B and D is the same. So no current flows through the galvanometer, i.e., I g = 0. It can be shown that the following equation is true. R R 3 (4) R R 4 If three resistances R, R, ) are known, the value of the fourth can be calculated. ( R3 The resistance of the thermistor ( R T ) at various temperatures (T Kelvin) can be measured using the bridge circuit. If we plot a graph between / T along the x-axis and ln( R T ) along the y-axis it will be a straight line since the following is true. E g ln( RT ) ln( R0 ) (5) k T The slope of the line is ( E /k.). g If the graph is between following. / T and log 0 RT, then the slope of the straight line is given by the E g k.303 (6) The energy gap is calculated from the slope of the straight line. Here E g k (Slope of the straight line) (7) E g is expressed in electron volts. 7

18 Physics Laboratory II SAQ. List a few metals, semiconductors, and insulators that you are familiar with.. Distinguish between metals, semiconductors and insulators in terms of energy gap..4 PRECAUTIONS (a) Care should be taken not to damage the balancing instrument. You can do this by using a high resistance in series with the galvanometer when the bridge is too for away from the balance. You can then remove this when the bridge is near the balance condition, by short-circuiting the high resistance. (b) Care should be taken to keep the thermocouple and thermistor in the same location during the calibration..5 EXPERIMENT.5. Calibration of thermistor APPARATUS: As in Section.. Fig..4 PROCEDURE: Take the given thermistor, and measure its resistance with the help of a multimeter at room temperature. Solder its ends to long connecting wires. Connect this thermistor to one arm of the 8

19 A Study of Network Theorems bridge (between C & D of Fig..3) and place known resistance boxes in the other three arms. The voltage source (battery), with a plug key in series, is connected across one diagonal of the foursided arrangement. A sensitive galvanometer or null detector or headphone and a high resistance (about 5000 ohms) is connected across the other diagonal as shown Fig..3. Now you can measure the resistance of the thermistor with the help of this bridge as follows: Make R and R, each equal to K ohm and R 3 = 0, and close the key K and then K, the key K 3, in the safety resistance being left open. The high resistance is then included in series with the balancing indicator and it cuts down the current to a low value. Note to which side the pointer moves on closing K. Repeat by having in R 3 the largest possible resistance or say 0000 ohm. Note the direction of the deflection. The galvanometer needle must deflect in the opposite direction for R 3 = 0 and R 3 = infinity. If it is so, the network is connected correctly. Otherwise check the connection again. Now take R R = K ohm. Vary R 3 till this deflection is brought to zero. When the deflection is almost nil, short-circuit the high resistance. Now the measuring instrument becomes more sensitive and a large deflection is seen. Make final adjustment of R 3 needed for perfect balance (no movement of pointer). Then R 3 is equal to R4 at room temperature. In this way you determine the value of the thermistor resistance at a given temperature. Now compare the resistance of this thermistor as measured by a digital ohm-meter and the value from the above bridge measurement. Is there any difference? Give reasons. Now you take the thermocouple, connect it to a millivoltmeter, or you can connect it with a digital multimeter in millivolt range. Mount the thermistor and thermocouple at the same location with the help of insulation tape. Insert them into a test tube. Dip this test tube in an oil bath and fix it on a stand. Now, immerse the oil bath (the test tube with the thermistor and thermocouple) into a large vessel of water and heat the water to boiling point, with the help of a burner. Now measure the voltage across the thermocouple in steps of 0. volt and measure the corresponding thermistor resistance using the bridge as described above. In case the change in the resistance of the given thermistor is very small, then you can connect an OP AMP configuration as shown in Fig..5 (For detailed discussion see the experiment on Operational Amplifiers.) To thermistor Output voltage Fig..5 9

20 Physics Laboratory II Record your data in Table I. Table I Resistance of the thermistor at room temperature =... S.NO Voltage across the Thermocouple Resistance across the thermistor WHEN HEATING WHEN COOLING WHEN HEATING WHEN COOLING The values of thermo-emf for different temperatures for a copper-constantan thermocouple is given in Table II. TABLE II Thermo-emf of Copper-Constantan thermocouple. Temp in C. emf in millivolts. TEMP emf With the help of the Table II you can plot a graph between voltages and temperatures of the thermocouple. From this graph, you will note the temperatures corresponding to the voltages which you have recorded earlier. Record temperature and resistance data in the Table III. TABLE III S. No. Temperature of the thermistor (T) Resistance (R) Plot a graph between temperature vs resistance on the following graph. This is the calibration chart of the given thermistor. 0

21 A Study of Network Theorems.5. Calculation of Band Gap Energy of a Thermistor PROCEDURE Take temperature vs resistance data of the given semiconductor. In this case we will use the data of the previous part of this experiment. Use the data from the observation Table III. Now, find the reciprocal of temperature and log 0 R. Record these values in observation Table IV. Table IV S. No. / T log R 0 Now plot a graph between given below: / T on the x-axis and log 0 R on the y-axis. Plot this graph in space You will find this to be straight line. Calculate the slope of this line. Put the value of this slope in Equation (7) and calculate the value of E. RESULT The band gap energy E g of the given thermistor is..... ev. g SAQ What do you mean by the energy gap in a semiconductor? Can you calculate this gap in a metal or an insulator? If not, why not?.6 CONCLUSIONS In this experiment you have studied bow a thermistor can be used as a temperature transducer and also some of the material properties of the thermistor materials, resists nee-temperature characteristics and the energy gap of toe semiconducting material. Is this energy band gap

22 Physics Laboratory II temperature-dependent or not? Can you think of using this thermistor for temperature measurements in any real-life situation? Write some examples

23 A Study of Network Theorems (For Counsellor's use only) Grade... Evaluated by. Name..... Enrolment Number EXPERIMENT 3 CONSTRUCTION AND CHARATERISATION OF POWER SUPPLIES & FILTERS Structure 3. Introduction Objectives 3. Apparatus 3.3 Study Material 3.4 Precautions 3.5 The Experiments Half Wave Rectifier Full Wave Rectifier Capacitor Input Filter Inductor Filter LC and PI Filters 3.6 Conclusions 3. INTRODUCTION You have seen in daily life many electronic instruments including domestic electronics like radio, tape recorders, T.V, amplifiers, musical keyboards etc. Do you know whether these instruments work on D.C. (Direct Current) or A.C. (Alternating Current)?. In fact they all operate on D.C. So when we connect such equipment to the mains (A.C.), it is necessary to convert this A.C. into D.C. In all these electronic instruments there is a section inside the equipment, known as the power supply section which converts this A.C. into D.C. with the help of rectifiers etc. This rectified voltage is pulsating and has some (small) A.C. component. It is desirable to convert this pulsating D.C. into constant D.C. and reduce the A.C. component of the rectified voltage so that the output is a pure D.C. voltage. This is accomplished by means of filters, which are composed of suitably connected capacitors, inductors and their combinations in different ways. The effectiveness of the filter is given by the RIPPLE FACTOR Y- It is defined as the ratio of rms* value of the A.C. component of the voltage to the D.C. voltage (or average value of the voltage). In this way we can identify the purity of the D.C. output in terms of ripple factor. It is desirable that the ripple factor is as small as possible. The capacitance filter has low ripple at heavy loads, while the inductor filter has low ripple at small loads. Depending on the requirements suitable filters can be selected. * The rms of value of A.C current it one that will produce the same quantity of heat as that of a D.C current. The voltage measured using the A.C. range in multimeter gives the rms value of the A.C. voltage. In the first part of the experiment we will construct half-wave and full-wave rectifiers and observe the waveforms on the cathode ray oscilloscope (C.R.O.). Then we will use capacitors and inductors as filters and observe the waveforms on the C.R.O. We will also measure the output voltages (both D.C. and A.C.) with the help of a multimeter and then calculate the ripple factor of these two filters. In laboratories not equipped with CRO, only multimeter readings nerd be used. 3

24 Physics Laboratory II In the second part of this experiment we observe the effect of L and PI ( ) filters on the output waveform of a full wave rectifier and then calculate the ripple factors in these two filters. Objectives After doing this experiment you will be able to: Design and construct half and full wave rectifier using step-down transformer and diodes. Show the output waveform of a full wave and ha If wave rectifier on a CRO screen. Show the effect of the filter (capacitor, inductor, Land PI filter) on the output voltage of a rectifier and compute ripple factor. Distinguish between output of L and PI filters. Trouble-shoot a power supply when it is defective. 3. APPARATUS. Centre-tapped transformer ( 9 V V). Diodes - four numbers - (IN4007 or BY6 or BY7) 3. Electrolytic capacitors (000/<F, 5 V) 4. Inductors - (50 rnh ) 5. Resistors - (00 - ) 6. Connecting wires, soldering iron, soldering flux (rosin), lead (solder) 7. CRO 8. Multimeter etc., 3.3 STUDY MATERIAL 3.3. Half Wave Rectifier Fig.3. Consider the circuit given in Fig 3., where we have used a step-down transformer, a semiconductor diode and a load resistance. A sinusoidal 9 V from a step-down transformer is applied across the series-connected diode D and the load resister R L. The input voltage V in is an A.C. voltage which changes its polarity every /00 sec. During the positive alternation the anode is positive (forward biased) with respect to the cathode and the current flows through the diode. During the negative alternation there is no current, because the anode is negative with respect to the cathode (reverse biased). The variation of current through the diode will result in the variation of voltage drop across R as shown in the Fig.3.. L 3.3. Full Wave Rectifier Here we use a centre tapped step-down transformer and two diodes to achieve full wave rectification as shown in Fig.3.. 4

25 A Study of Network Theorems Fig. 3. At any moment during a cycle of V in if point A is positive relative to C, point B is negative relative to C. The voltage applied to the anode of each diode is equal but opposite in polarity at any given instant. When A is positive relative to C, The anode of D is positive with respect to its cathode. Hence D will conduct but D will not. During the second alternation, B is positive relative to C. The anode of D is therefore positive with respect to its cathode, and conducts while D will not. There is conduction by either D, or D during the entire input - voltage cycle. Since the two diodes have a common-cathode, load resistor R L the output voltage across R L will result from the alternate conduction of D and D. The output waveform V across R L is shown in Fig. 3.. The output of a full wave rectifier is also pulsating direct current as seen from the Fig Capacitor Input Filter Capacitor input filter is shown in Fig. 3.3.b. Here the high value capacitor is connected across the output voltage. The working principle is as follows. 5

26 Physics Laboratory II The output of the rectifier contains both A.C and D.C. When the capacitor is connected across the output terminal, A and B in Fig. 3.3.a, A.C. components arc by-passed while the D.C. component is blocked and they develop a voltage across the capacitor. Now the capacitor is discharged through the load resistance R L which is of high value. So it delivers continuous D.C. across the load resistor Inductor Filters Connect between A and B in Fig. 3.3.a inductor L and the load resistor R L given in Fig. 3.3.c. The impedance of an inductor is equal to fl, where f = frequency and L = inductance. If both A.C. and D.C. are flowing through an inductor, it has a high impedance for A.C. but not for D.C. So we will find a constant D.C. voltage across the load. In this way it will remove ripples (i.e. A.C. components) and convert pulsating D.C. into constant D.C. The ripple factor can be further reduced by a combination of inductor and capacitor. The combination of L and C given in Fig.3.3.d is known as LC filter and the combination of L and C shown in Fig. 3.3.e is known as a section LC filter. 3.4 Precautions (a) While measuring voltages using multimeters, select the correct/appropriate ranges and keep the selector knobs in the correct position. (b) Check the polarity of the diode using the multimeters and make sure that you have connected them correctly. How to check? (c) Make sure that you are connecting the electrolytic capacitor with correct polarity. (d) Soldering should be done perfectly. 3.5 THE EXPERIMENT 3.5. Half Wave Rectifier To construct a half wave rectifier and observe the output waveform using a CRO and measure the output voltage. APPARATUS Step-down transformer, diode, resistors, soldering iron, solder and rosin. Step () Check the continuity of the primary and secondary winding of the step-down transformer. Step () Find the polarity of the diode using the multimeter. (By applying either forward bias or reverse bias one can identify the polarity of the diode.) Note: Other ways of identifying the polarity of the diode. (a) A band at one end of the diode indicates cathode (e.g., IN4007) as shown in Fig.3.4. Fig

27 A Study of Network Theorems (b) A Flat portion in a diode like BY6 or BY7 is anode and the curved end or an arrow shaped portion is cathode as shown in Fig.3.5. Step (3) Connect the circuit as shown in Fig 3.. Fig. 3.5 Step 3(c) Give input voltage (0V A.C) Step 4 Measure the A.C. input voltage, A.C. output voltage and the rectified voltage across the load resistance R L using a multimeter. Step 5 The output voltage across R L is given to the Y-Y input of the CRO. Adjust the appropriate knobs to get the wave pattern of the output. Trace the output on a tracing paper, and paste it in this report, below. Compare the figure with the expected figure Full Wave Rectifier To construct a full wave rectifier and observe the output waveform using a CRO and measure the output voltage. PROCEDURE Take a centre-tapped step-down transformer (9V - 0-9V) Step Follow step and of the experiment in Section 3.5. (Here two diodes have to be checked) Step Connect the circuit as given in Fig. (3.). Step 3 Measure the A.C. input voltage, A.C. output voltage and the rectified (D.C) voltage across the load resistance R L using a multimeter. 7

28 Physics Laboratory II Step 4 Voltages across R L, Diode, and Diode are measured using a CRO as in the experiment in section Trace the output waveform on a tracing paper, and paste it in this report in the space below Capacitor Input Filters To study the capacitor filter and calculate the ripple factor and record the output wave form with and without filters. Step Connect a high value (000 F, 5 V) capacitor (electrolytic capacitor) across R L as shown in Fig. 3.3.b and connect it between A and B as shown in Fig 3.3.a. The circuit has only a simple capacitor filter. Step Measure the D.C. and A.C. voltage across R L. Repeat the experiment for different R L values and calculate the ripple factor for each load and tabulate the values. Table I S. No. Load Output (d.c) Voltage Output (a.c) Voltage ripple factor E E rms dc 8

29 A Study of Network Theorems Step 3 Record the waveform of the output voltage with and without capacitor (trace it from the CRO screen and paste it below). SAQ Note down your observations when you compare the waveform of the output with and without the capacitor Inductor Filters To study the inductor filter and calculate the ripple factor. Step Follow step and of the experiment in Section Step With the circuit given in Fig. 3.3.a, between A and B connect the circuit given in Fig. 3.3.c. Here the inductor is connected in series. The circuit is called inductor filter. Step 3 Connect the primary of the transformer to the mains and measure the output voltage across R L (both A.C. and D.C). Repeat the experiment for different load values and tabulate your data: 9

30 Physics Laboratory II S. No. Load Output (d.c) Voltage Table II Output (a.c) Voltage ripple factor E E rms dc LC and Filters To study LC and filters and compare the ripple factor in these two filters. Procedure: In the previous part of the experiment you have used an inductor as a filter. Now, connect a capacitor in parallel to the load resistance as shown in Fig. 3.3.d. This combination of inductor and capacitor is known as an LC filter. Now measure D.C. and A.C. voltages across the load as measured in the previous part of this experiment. Repeat the experiment for different load resistances and record your data in Table III. Calculate the ripple factor for each load. TABLE III S. No. Load Output (d.c) Voltage Output (a.c) Voltage ripple factor E E rms dc 30

31 A Study of Network Theorems Now connect the output of load resistance R L to the Y plate of the oscilloscope. You will find the output waveform. Now, you trace these waveforms on a tracing paper and paste in the space given below: SAQ Compare the waveform of C, L and LC filter. Write your conclusion in the space below: SAQ What is the difference in the ripple factor in I, C, and C filter? Now connect one more capacitor before the inductor, in parallel to the previous capacitor. It is shown in Fig.3.3.e. Such a combination is known as a filter. Now measure D.C. and A.C. voltages across load resistance R L as measured in the above part of this experiment. Repeat the experiment for different load and record your data in Table IV. Calculate the ripple factor for different loads. 3

32 Physics Laboratory II S. No. Load Output (d.c) Voltage Table IV Output (a.c) Voltage ripple factor E E rms dc Write your conclusion in the space given below: Now connect the output of the load resistance R L to the Y-Y input of the oscilloscope. You will find the output waveform. Now, you trace this waveform on a tracing paper and paste in the space given below: SAQ From your data find the difference between the waveforms of the LC and filters. Write your conclusion in the space given below: Note: Due to technological advancement, the present day power supplies are made more compact by using integrated chips (like 7905) for power regulation instead of all kinds of filters. 3

33 A Study of Network Theorems 3.6 CONCLUSIONS You have constructed half and full wave rectifiers and smoothed the output using different types of filters. Now answer the questions below in a brief manner. (a) What will happen if you give an unfiltered voltage to a radio set? (b) At heavy loads which kind of filter is preferable? (c) How will you check the polarity of a semiconductor diode? (d) How does an inductor filter work? 33

34 Physics Laboratory II (For Counsellor's use only) Grade... Evaluated by. Name..... Enrolment Number EXPERIMENT 4 STUDY OF OPAMP AS SUMMING AND INVERTING AMPLIFIER 4.. Introduction Objectives 4.. Apparatus 4.3. Study Material Stages of an Opamp Use of Negative Feed Back Opamp as a Half Wave Rectifier Opamp Specifications Types of Opamps 4.4 Precautions 4.5 The Experiments Inverting Amplifier Summing Amplifier 4.6 Conclusions 4. INTRODUCTION Given below is a list of some systems and equipment that I hope you have seen and/or used in your everyday life. (a) A radio set (b) A doctor's stethoscope (c) An electrocardiography (ECG) machine (d) A microscope (e) A public address system. I am sure you will be surprised if I ask you what is common in all the above equipment? The answer is "Some sort of an amplifier". In a radio set, we have an amplifier which amplifies very small electrical signals (of the order of a few millivolts). These signals are received from distant radio stations. Not only that, you can even change the amplification by turning the volume control. In a doctor's stethoscope, sound of heartbeat is amplified. In an ECG, we have amplification of small electrical signals (a few microvolt) given out by the heart. A microscope is an optical instrument to see amplified (magnified) images of very small, microscopic objects. In a public address system, speech is given to the microphone by the person speaking. Speech is converted into electrical signals, amplified and fed to the loudspeaker. Thus, in all above examples, we have some type of amplifier. Today you shall study a special type of amplifier, to amplify electrical signals, called an Operational Amplifier (Opamp). Opamps may be treated as multipurpose devices which may be used as amplifiers, oscillators, differentiators, integrators, and can also perform other mathematical operations like addition, subtraction, multiplication etc.(and hence the name Opamp).They are very extensively used in present day electronics ranging from entertainment electronics to medical instrumentation and computers. 34

35 A Study of Network Theorems In this laboratory, we will carry out some simple experiments on an Opamp illustrating some-of its elementary characteristics. Objectives After performing this experiment you will be able to use an Opamp as: Inverting amplifier Summing amplifier 4.. APPARATUS nos. - Variable power supplies of +5 V and -5 V. nos. - Drycells of.5 V each. no. - Digital multimeter for both a.c and d.c measurements. nos. - Rheostats, or Potentiometer, Resistance, 0 K ohms each. no. - Half-watt resistance of different values like 4.7 K ohm, 0 K ohm etc. nos. - Switches. no. - Oscilloscope. no. - Opamp C 74, with socket. 4.3 STUDY MATERIAL 4.3. Stages of OPAMP The opamp is a high gain direct coupled amplifier, has high input impedance and low output impedance. Multiple applications of the opamp are made possible by the external control of the variable feedback employed in it. Feedback means that some or all of the output is connected to one of the inputs. The connection may be simple or it may be through a complicated circuit. Fig.4..shows the symbol for an opamp. It has two inputs marked. Fig. 4. The (-) input is called the "inverting input" The (+) input is called the " non-inverting input". A signal applied to the ( ) input will be shifted in phase by 80 at the output. It means that if a -ve pulse is given at inverting input it will appear as a +ve pulse at the output. On the other hand, a signal applied to the non-inverting (+) input will appear in the same phase at the output. This is shown in Figs.4. and 4.3, for inverting and non-inverting cases, respectively. Fig.4. 35

36 Physics Laboratory II Fig.4.3 Though from the point of using the opamp it is not necessary to go into the details of the inside circuits of the opamp, but from the point of view of learning one may understand its working with reference to the block diagram shown in Fig.4.4. Fig.4.4 STAGE The first stage of an opamp is a difference amplifier. For most of the parameters like open loop gain, input impedance etc., we refer to the data sheet provided at the end of this experiment. The difference amplifier amplifies the difference between the two input signals. It is an amplifier that could amplify a small difference in voltage between the inputs, even if the inputs themselves may be at a few volts above ground. For example, if the terminal marked -ve is at +.0 volt DC and the other at +.00 volts DC, the difference 0.0 volt DC alone will be amplified. A well designed difference amplifier is not sensitive to environmental changes. The output signal from a difference amplifier is proportional to the difference between the two input signals. The mode of operation in which two different signals are applied at the inputs to get an output signal proportional to the difference of the two input signals is called "differential input differential output mode". The difference amplifier may also be used in a single ended output mode if one of the two inputs is grounded. When the +ve input (non-inverting) is grounded, a +ve input signal at the inverting input will appear as a-ve signal at the output (see Fig.4.5). This is referred to as "single ended input single ended output inverting mode". Similarly, if the inverting input is grounded and a signal is applied at the noninverting input it will appear at the output without any phase change. The operation will be termed as "single ended input single ended output noninverting mode". 36

37 A Study of Network Theorems Fig.4.5 If in differential mode operation inputs V and V are applied respectively at the inverting and non-inverting inputs such that V V V the differential gain A d is given by A d Voutput Voutput () V V V ) input ( On the other hand under ideal conditions the output of the differential amplifier should be zero if identical signals (equal in amplitude and phase) are applied to the two inputs of the amplifier. In practice, however, this ideal condition of zero output signal is not achieved. One gets some output signal even when identical signals are applied at both inputs. The gain A c in this condition is given by A c V output () ( V V ) The ratio A d /A c is called the common mode rejection ratio (CMRR). It is an index of the ability of the amplifier to reject signals common to both the inputs. In other words CMRR may be looked on as the quality factor of the amplifier to select proper signals out of a mass of noise common to both the inputs. The range of the common mode voltage over which the difference amplifier works properly is called the common mode voltage range. STAGE Stage is the second amplifier and may be another difference amplifier with single ended input mode. It provides further gain. STAGE 3 The third stage in the opamp is the "level shifter". Since each stage in the opamp is directly coupled to the next stage, the dc level increases from one stage to the next and ultimately 37

38 Physics Laboratory II approaches the power supply voltage. The level shifter stage provides compensation for this rise in the dc level. STAGE 4 The last stage is the output power amplifier. It has high current gain, wide band width and low output impedance Use of negative feedback The output of the opamp is always inverted with respect to the inverting input. If a small amount of output is fed back (added) along with the inverting input, it will result in a feedback called negative feedback. Multiple applications of the opamp a re made possible by the external control of the negative feed back. The basic feedback circuit is shown in Fig.4.6.a. As shown, the output is fed back to the inverting input through a resistance R. This provides negative feedback. Suppose a signal is applied at the inverting input as in Fig.4.6.a. f Fig. 4.6.a Fig. 4.6.b The output will be an amplified and inverted signal. A part of this output signal which is 80 out of phase with the input is fed back at the inverting input through resistance R F and hence negative feed back lakes place. It is also possible to use the opamp as a non-inverting amplifier by 38

39 A Study of Network Theorems applying signal to the (+) input (non-inverting), as shown in Fig.4.6.b. It may, however, be noted that the feed back network (resistance R F ) is still connected to the inverting input. From the detailed analysis which is beyond the scope of the present discussion it can be shown that for the arrangement of Fig.4.6,a, (inverting amplifier) the output voltage V output is given by V output ) R F ( Vinput (4) RR here V input is the input voltage and the -ve sign represents the phase change of 80. For the non-inverting amplifier circuit of Fig. 4.6.b the total output voltage V output is given by V output R F Vinput (5) RR the +ve sign in the above equation indicates no phase change. As such the gains for the inverting and the non-inverting amplifier circuits are respectively Ginv and Gnon inv is given by R G ) G F inv ( (6) RR R F non inv (7) RR It may be noted that apart from the phase term (-ve or +ve) the gain of the inverting and noninverting configurations are different. A careful study of the circuits of Fig.4.6.a and Fig.4.6.b for inverting and non-inverting amplifier configurations will tell that the two circuits are identical except for the interchange of input terminals and the ground connections. The expressions for the gain differ because in inverting configuration resistances R F and R R form a voltage division network for both the input signal V and the signal fed back from output to the input through R F. In the non-inverting configuration Fig. 4.6.b the voltage division takes place only for the feedback signal and not for the input signal. The following numerical examples will make things more clear. (a) Suppose in Fig.4.6.a R R =.5 k ohm and R F = 0 k ohm, then the gain is given by RF 0 G inv ( ) ( ) (8) R.5 R i.e., the output signal will be amplified by a factor of 4 but will get out of phase by 80 w.r.t the input. One may use both a.c. and d.c. signals at the input. 39

40 Physics Laboratory II (b) If R R = R F the gain will be unity, and the signal in the output will be of the same magnitude but in opposite phase. (c) If RR RF, G inv will be. Do you know why? Write a possible reason. In all above three cases one can see that by controlling the ratio of R F and R R, an output signal of increased amplitude, same amplitude or of diminished amplitude may be obtained, but the phase change is always 80. In a similar way for the non-inverting amplifier configuration if (a) R = 0Kohm, R =.5 K ohm F R 0 G non inv = 5 (9) 5 (b) For the case RF R R = 0 K ohm (say) G =, and for non inv (c) (d) RR RF. non inv G will always be greater than unity. In the extreme case when in non-inverting configuration R 0 and R (see Fig.4.7) F R G 0 (0) non inv So in this configuration the output voltage is equal in amplitude and in phase with the input. This is called the voltage follower circuit. Mathematical operation of summing may also be performed by the opamp, using the connection shown in Fig

41 A Study of Network Theorems Fig. 4.7 Fig. 4.8 The gain of the above circuit is given by RF RF V V R R G () V V ) ( If R F R R, then the gain G =, and therefore V output ( V V ) which is the sum of input voltage signal. This will be true even if V and V are of opposite sign, so this is really an algebraic summing circuit. The output voltage may be made equal to the sum of input voltages V and V, each scaled by some multiplying constant, by choosing the values of R F, R and R. For instance, R R. R F 3 4

42 Physics Laboratory II OPAMP as a Half-Wave rectifier and as an Electronic Ammeter Opamp half-wave rectifier circuit is shown in Fig.4.9. This is a modified version of Fig.4.7, with diode inserted in the output. When the output is positive, the diode conducts and the circuital acts exactly as Fig.4.7. The gain is, and the positive part of the signal is faithfully given to the output. When the output is negative the diode does not conduct. The output is effectively disconnected from the opamp, and only connected to ground through the resistor. Thus the circuit acts as an amplifier for only positive signals. It acts as a half-wave rectifier. So does a diode by itself! But in the opamp circuit the signal source always faces a high-impedance amplifier input. With a simple diode the source is short-circuited on positive inputs. Fig.4.9 In the following circuit diagram (Fig.4.0) an opamp works as an electronic ammeter. The input voltage V i applied to the left end of R causes a current A i to flow in the input circuit. It is this current which is to be measured. The output voltage of the opamp is V O. Thus the output voltage is proportional to the current A i and does not depend on action for which the circuit is called an "electronic ammeter". R R. This is the Fig.4.0 4